Problem: $A$ $B$ $C$ If: $ AB = 7x + 6$, $ AC = 104$, and $ BC = 5x + 2$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {7x + 6} + {5x + 2} = {104}$ Combine like terms: $ 12x + 8 = {104}$ Subtract $8$ from both sides: $ 12x = 96$ Divide both sides by $12$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $BC$ $ BC = 5({8}) + 2$ Simplify: $ {BC = 40 + 2}$ Simplify to find ${BC}$ : $ {BC = 42}$